1. Model specification

The following equation was obtained in a study of students' test scores:

SCORE = 756.10 + 19.30hsize - 2.19hsize2 - 45.09female - 68.81alien + 62.31female*alien

(6.29) (3.83) (0.53 (4.29) (12.71) (18.15)

n=4137 R2=0.0858. Standard errors are in parentheses.

The variable SCORE is the test score, hsize is size of the student's high school graduating class, in hundreds, female is a gender dummy variable (equals 1 for women and 0 for men), and alien is a country of origin dummy variable equal to one for international (foreign) students and zero for native students.

(a) What is the interpretation of the variable hsize?

(b) Is there a strong evidence that hsize2 should be included in the model? Based on this equation, can you say anything about the optimal high school size?

(c) Holding hsize fixed, what is the estimated difference in the test score between native females and native males? How statistically significant is this estimated difference?

(d) What is the estimated difference in the test score between native males and alien males? Test the null hypothesis that there is no difference between their scores, against the alternative that there is a difference.

(e) What is the estimated difference in the test score between alien females and native females? What would you need to do to test whether the difference is statistically significant?